Solve for $x$ and $y$ using elimination. ${-5x-3y = -53}$ ${4x+3y = 46}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $-x = -7$ $\dfrac{-x}{{-1}} = \dfrac{-7}{{-1}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-5x-3y = -53}\thinspace$ to find $y$ ${-5}{(7)}{ - 3y = -53}$ $-35-3y = -53$ $-35{+35} - 3y = -53{+35}$ $-3y = -18$ $\dfrac{-3y}{{-3}} = \dfrac{-18}{{-3}}$ ${y = 6}$ You can also plug ${x = 7}$ into $\thinspace {4x+3y = 46}\thinspace$ and get the same answer for $y$ : ${4}{(7)}{ + 3y = 46}$ ${y = 6}$